1. Field
This application relates generally to simulating a fluid flow over a computer-generated surface and, more specifically, to predicting whether a point on the surface is adjacent to laminar or turbulent flow.
2. Description of the Related Art
Aerodynamic analysis of an aircraft moving through a fluid typically requires an accurate prediction of the properties of the fluid surrounding the aircraft. Accurate aerodynamic analysis is particularly important when designing aircraft surfaces, such as the surface of a wing or control surface. Typically, the outer surface of a portion of the aircraft, such as the surface of a wing, is modeled, either physically or by computer model, so that a simulation of the fluid flow can be performed and properties of the simulated fluid flow can be measured. Fluid-flow properties are used to predict the characteristics of the wing, including lift, drag, boundary-layer velocity profiles, and pressure distribution. The flow properties may also be used to map laminar and turbulent flow regions near the surface of the wing and to predict the formation of shock waves in transonic and supersonic flow.
A computer-generated simulation can be performed on a computer-generated aircraft surface to simulate the fluid dynamics of a surrounding fluid flow. The geometry of the computer-generated aircraft surface is relatively easy to change and allows for optimization through design iteration or analysis of multiple design alternatives. A computer-generated simulation can also be used to study situations that may be difficult to reproduce using a physical model, such as supersonic flight conditions. A computer-generated simulation also allows a designer to measure or predict fluid-flow properties at virtually any point in the model by direct query, without the difficulties associated with physical instrumentation or data acquisition techniques. In this way, computer-generated simulations allow a designer to select an aircraft surface design that optimizes particular fluid-flow characteristics.
In some cases, a portion of an aircraft surface, such as a wing surface, can be optimized to maximize regions of laminar flow. A region of fluid flow may be considered laminar when the flow tends to exhibit a layered or sheet-like flow. In laminar-flow regions there is little mixing between the layers or sheets of fluid flow having different fluid velocities. Laminar flow can be contrasted to turbulent flow, which tends to exhibit chaotic or erratic flow characteristics. In turbulent-flow regions there is a significant amount of mixing between portions of the fluid flow having different fluid velocities.
Near the surface of a wing, the fluid flow typically begins as laminar flow at the leading edge of the wing and becomes turbulent as the flow progresses to the trailing edge of the wing. The location on the surface of the wing where the fluid flow transitions from laminar to turbulent is called a transition point. The further the transition point is from the leading edge, the larger the region of laminar flow.
There are many advantages to aircraft utilizing laminar flow over large portions of the fuselage and wing surfaces. In general, laminar flow dissipates less energy than turbulent flow. Increasing the proportion of laminar flow regions over a wing surface reduces drag, and therefore, reduces fuel burn, emissions, and operating costs.
According to one model, the transition to turbulent flow is caused by the growth of instabilities in the boundary-layer fluid flow adjacent to the aircraft surface. These instabilities may be initiated by, for example, surface contamination, roughness, vibrations, acoustic disturbances, shockwaves, or turbulence in the free-stream flow. The instabilities start out as small, periodic perturbations to the fluid flow near the aircraft surface, then grow or decay depending on the properties of the boundary layer, such as flow velocity and temperature profiles. At first, when the instabilities are small, their behavior is similar to sinusoidal plane wave instabilities and can be described by linearized perturbation equations. As the unstable modes grow in amplitude, nonlinear interactions become dominant. Following the nonlinear growth, the laminar instabilities begin causing intermittent spots of turbulence, which spread and eventually merge together, resulting in a fully turbulent boundary layer.
When predicting the location where a laminar flow transitions to turbulent flow, designers may consider many different types of instabilities. These types include Tollmien-Schlichting (TS) wave instabilities and crossflow vortices. The type of instability may depend, in part, on the geometry of the aircraft, such as the degree of sweep of the wing.
For a given instability type (e.g., TS wave or crossflow vortex), there are typically multiple individual instability modes that may be defined using mode parameters, such as temporal frequency and/or spatial spanwise wave number. By considering a range of individual instability modes when simulating a fluid flow around the aircraft surface, designers may account for a variety of potential instability sources.
In general, transition prediction techniques allow a designer to estimate the point on an aircraft surface where laminar flow first transitions to turbulent flow. In some cases, designers may attempt to maximize regions of laminar flow by designing the surface of the wing so that the transition point is as far from the leading edge as possible. Producing useful results often requires running complex simulations over a wide range of design variables and flight conditions. Unless the transition prediction technique is efficient and easy to use, running multiple complex simulations may be prohibitively time-consuming in the earlier stages of aircraft design where major configuration changes are likely.
One transition prediction technique is based on linear stability theory (LST), which may be used to model the growth of instabilities in a boundary-layer fluid flow around a computer-generated aircraft surface. LST models these instabilities as spatio-temporal waves that are amplified or attenuated as the flow progresses along the boundary layer. This modeling requires the solution of an eigenvalue problem. Input to an LST-based analysis includes a boundary-layer solution and values parameterizing a selected instability mode (e.g., wave number and frequency). The input boundary-layer solution includes, for example, boundary-layer properties such as flow velocity and temperature and can be determined using a time-invariant computational fluid dynamics (CFD) simulation module. As an output, LST-based analysis computes an instability local growth rate associated with the selected instability mode at a given point on the aircraft surface.
While LST-based analysis may produce accurate results, LST-based analysis may be prohibitively time-consuming in early design phases. LST-based analysis may require the user to interact with the analysis frequently to check for lost modes and nonphysical results. This interaction is not only time-consuming, but also requires that the user have experience interacting with the specific implementation of the LST-based analysis. Thus, even with powerful computing resources, LST-based analysis may be impractical when iterating through a large number of design configurations in the early phases of aircraft design.
In contrast to those based on LST-based analysis, there are other transition prediction techniques that require very little user interaction but may sacrifice accuracy or reliability. Without high accuracy and reliability, these techniques are less useful for iterating design configuration in the early phases of aircraft design.
The techniques described herein can be used to generate a growth-rate model that reduces or eliminates the need for user interaction. Further, iteration of the techniques described herein can be used to provide a prediction of the transition point on a computer-generated aircraft surface.